suppose a model of the ship the queen mary is 17 inches in length. the actual length of the queen mary is 1020 feet. what is the scale of the model?
The Correct Answer and Explanation is :
To find the scale of the model of the Queen Mary, we need to compare the length of the model to the actual length of the ship. The model is 17 inches long, while the actual Queen Mary is 1020 feet long.
First, we should convert the actual length from feet to inches since our model’s length is in inches. There are 12 inches in a foot, so:
[
1020 \text{ feet} \times 12 \text{ inches/foot} = 12,240 \text{ inches}
]
Now that we have both lengths in inches, we can calculate the scale by setting up a ratio of the model’s length to the actual length:
[
\text{Scale} = \frac{\text{Model Length}}{\text{Actual Length}} = \frac{17 \text{ inches}}{12,240 \text{ inches}}
]
Next, we simplify this ratio:
[
\text{Scale} = \frac{17}{12,240}
]
Calculating this gives us:
[
\text{Scale} \approx 0.00139
]
To express this as a scale ratio, we can take the reciprocal:
[
\text{Scale} = \frac{12,240}{17} \approx 720
]
Thus, the scale of the model is approximately 1:720. This means that 1 unit of measurement on the model corresponds to 720 of the same units on the actual ship.
Explanation
The scale model serves as a simplified representation of the actual object, allowing easier visualization and handling. In this case, the Queen Mary is a massive ocean liner, and creating a model that is the same size would be impractical. By scaling it down to a manageable size (1:720), we can still appreciate the ship’s features and details without needing excessive space or resources.
The scale is calculated by comparing the lengths directly, converting all measurements to the same units to ensure accuracy. The derived scale of 1:720 tells us that every 720 inches on the real ship corresponds to just 1 inch on the model. This is a common practice in model making, architecture, and engineering, where understanding the proportions of a large object in a smaller form can help in design, education, and visualization.